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The Effect of Vertical Temperature Gradient on the Propagation of Three-dimensional Waves in a Protoplanetary Disk

Excitation and propagation of waves in a thermally stratified disk with an arbitrary vertical temperature profile are studied. Previous analytical studies of three-dimensional waves had been focused on either isothermal or polytropic vertical disk structures. However, at the location in a protoplanetary disk where the dominant heating source is stellar irradiation, the temperature gradient may become positive in the vertical direction. We extend the analysis to study the effects of the vertical temperature structure on the waves that are excited at the Lindblad resonances. For a hotter disk atmosphere, the $f$-mode contributes less to the torque and remains confined near the midplane as it propagates away from the resonances. On the other hand, the excitation of the $g$-modes is stronger. As they propagate, they channel to the top of disk atmosphere and their group velocities decrease. The differences compared to previous studies may have implications in understanding the wave dynamics in a realistic disk structure.